I know that 10^-2.3=5.0 * 10^-3
How do I get 10^-2.6 in the same form as 5.0 * 10^-3?
please and thank you!
Punch in 10 on your calculator, then press the yx button followed by -2.6 and then press equal. You should get 2.51E-3
thanks, but mine just says: .0025118864
To express 10^-2.6 as 5.0 * 10^-3, you need to simplify it to the same base and exponent as the given form. Here's how you can do it:
1. Recall that any number in scientific notation can be written as a decimal multiplied by a power of 10.
In this case, 5.0 * 10^-3 can be written as 0.005 * 10^-3.
2. Convert 10^-2.6 to the same exponent of 10^-3 by multiplying both the numerator and denominator by 10^0.6.
10^-2.6 = (10^(-2.6 + 0.6)) * (10^(-3 + 0.6))
= 10^-2 * 10^-2.4
= 0.01 * 10^-2.4
3. Combine the decimal part with the power of 10 to express it in scientific notation.
0.01 * 10^-2.4 = 0.01 * (10^(-2 + 0.4))
= 0.01 * 10^-1.6
4. Multiply the decimal part by 10 to get a coefficient of 1.0. Multiply the exponent part by 10 to compensate.
0.01 * 10^-1.6 = 1.0 * 10^-3 * 10^(-0.6 + 0.6)
Therefore, 10^-2.6 can be expressed as 1.0 * 10^-3 in the same form as 5.0 * 10^-3.